Vector representations of graphs
Discrete Mathematics - In memory of Tory Parsons
A note on vector representation of graphs
Discrete Mathematics
Implicit representation of graphs
SIAM Journal on Discrete Mathematics
Efficient computation of implicit representations of sparse graphs
Discrete Applied Mathematics
On orthogonal representations of graphs
Discrete Mathematics
Compact Implicit Representation of Graphs
WG '98 Proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science
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We consider a simple model for representing a graph in computer memory in which every vertex is assigned a word in a finite alphabet - vertex code - and the adjacency of two vertices is a function Ψ of their codes. The function Ψ is called the representation function. We say that Ψ is universal if a Ψ-representation exists for every simple graph G. In this paper, we study representation functions computable by automata with two states. The main result is a criterion characterizing the universal functions. In the case of binary alphabet, we provide some bounds on the dimension of minimum Ψ-representation.